Least Common Multiple (LCM) of 90 and 160
The least common multiple (LCM) of 90 and 160 is 1440.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 90 and 160?
First, calculate the GCD of 90 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 160 = 0 remainder 90 |
| 2 | 160 ÷ 90 = 1 remainder 70 |
| 3 | 90 ÷ 70 = 1 remainder 20 |
| 4 | 70 ÷ 20 = 3 remainder 10 |
| 5 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 170 | 13090 |
| 42 and 158 | 3318 |
| 130 and 188 | 12220 |
| 28 and 24 | 168 |
| 20 and 119 | 2380 |